Question 635390
<pre>
The slower traveled at x miles per hour
The faster traveled at x+5 miles per hour

Their approach rate = the sum of their speeds = x+(x+5) = x+x+5 = 2x+5

Time = 1 hour 40 minutes = {{{1&40/60}}} hours = {{{1&2/3}}} hours = {{{5/3}}} hours.

Distance = (Rate)·(Time)
     100 = (2x+5)·{{{5/3}}}

Multiply through by 3

     300 = (2x+5)·5

Divide both sides by 5
    
      60 = 2x+5
      55 = 2x
    27.5 = x

The slower was going 27.5 miles per hour and the faster was going
5 miles per hour faster or 32.5 miles per hour.

Edwin</pre>